Question

Consider a binomial random variable with n = 9 and p = 0.3. Let x be the number of successes in the sample.
a. Find the probability that x is exactly 2.
b. Find the probability that x is less than 2.
c. Find P(x > 2).
d. Find P(2 ≤ x ≤ 4).

I've solved the a) but I can't get the other 3. I got 0.267 for a).

Answer 1

For B, note that P(x < 2) = P(x = 0) + P(x = 1) since these are the only two values the random variable can take below 2.

Answer 2

So do i have to do the same thing i did for part a but repeat it for x = 0 and x = 1?

Answer 3

Yep, since you know how to calculate the probability the variable is equal to something you can use that to find the probability it is less than something.

Answer 4

okay and for part c i do tht for x = 3 all the way up to 9? that would take forever...

Answer 5

For part C you can use the fact that P(x > 2) + P(x <= 2) = 1 and use your previous answers to calculate P(x > 2).

Answer 6

Otherwise you're right, it is a bunch of boring calculation :P

Answer 7

I dont understand

Answer 8

If something is not larger than 2, then that means it's less than or equal to 2. So P(x > 2) = 1 - P(x <= 2). From your first two answers you can calculate P(x <= 2) easily so that's why we do it this way.

Answer 9

Im sorry I still dont get it

Answer 10

That's ok, I'm just trying to think of ways to explain it :P Do you know that if you know the probability of something happening then the probability of it not happening is 1 minus that probability?

Answer 11

yeah

Answer 12

btw i think i solved part b is it 0.196?

Answer 13

It is :) So do you agree that P(x > 2) = 1 - P(x <= 2)?

Answer 14

I dont understand that formula

Answer 15

It comes from what I said above combined with the fact that is x is not > 2, then it is <= 2.

Answer 16

okay that makes sense

Answer 17

Alright. So can you find P(x <= 2)?

Answer 18

i did c9,1(0.3)^2(0.7)^9-1 and the same this for 0 to get 0.196

Answer 19

i used an online calculator to solve it because i dont know how to do it on my calclator

Answer 20

0.196 is P(x < 2), but you need P(x <= 2)

Answer 21

no part b says just less than 2
and i found out how to do it on my calculator had to use the nCr key

Answer 22

I mean for part C, since we know that P(x > 2) = 1 - P(x <= 2)

Answer 23

so would P(x <=2) be 0.267 + 0.196?

Answer 24

Yes. Then you can find the answer to C

Answer 25

so c would be 1 - (0.267+0.196)?

Answer 26

Yep!

Answer 27

Wow! thank you I actually understand what you were trying to say earlier

Answer 28

okay so how would i go about doing part d?

Answer 29

is it asking to find x = 3?

Answer 30

Well if 2 <= x <= 4 then that means x can be 2, 3, or 4.

Answer 31

right so how can i approach this?

Answer 32

would i have to solve for x = 2,3,4?

Answer 33

Yeah, I think the easiest way to do it here is to just calculate the probabilities for each case and sum them.

Answer 34

:( okay well atleast I know how to do these srot of questions thank you so much JE!

Answer 35

No worries, glad I could help! :)